Answer:
The coordinates of the epicenter are (1,2) ie x=1, y =2
Step-by-step explanation:
We use the fact that the distance d between 2 points, (C y₁) and (x₂, y₂) is computed by the Pythagorean formula:
(x₁ - x₂)² + (y₁ - y₂) = d²
Let the epicenter be located at (x, y)
Distance dA from point A(5,2) is known to be 4 and is given by the equation:
(x-5)² + (y - 2)² = dA² = 4² = 16 ==>
(x-5)² + (y-2)² = 16 (1)
Similarly, the distance from point B(-2,2) is given as 3. Therefore,
(x - (-2))² + (y-2)² = 3² = 9 or
(x + 2)² + (y-2)² = 9 (2)
Distance from point C(1,-3) ==>
(x-1)² + (y-(-3))² ==> (x-1)² + (y +3)² = 25 ...(3)
(1) - (2) cancels out the y terms and gives us
(x-5)² - (x+2)² = 7 (4)
This simplifies to
x² + -10x + 25 - (x² +4x + 4) = 7
or
x² + -10x + 25 -x² -4x - 4 = 7
-10x -4x = 7 - 21 = -14
Therefore, -14x = -14 giving us x = 1
Substituting for x = 1 in equation (3) gives us
(1-1)² + (y+3)² = 25 or
y + 3 = √25 = 5 giving y = 2
So we get the epicenter coordinates as x=1, y =2
Crosscheck in each of the equations (1), (2) and (3) for consistency
Equation 1 : (1-5)² + (2-2)² = -4² = 16 Check!
Equation 2: (1-(-2))² + (2-2)² = (1+2)² = 3² = 9 Check!
Equation 3: (1-1)² + 2-(-3))² = (2+3)² = 5² Check!
the formula for the circumference of a circl is c = 2 nr determine the circumference when the radius r is 10 cm
Answer:
20π cm or approximately 62.8 cm
Step-by-step explanation:
» Concepts
The circumference of a circle is the distance, or perimeter, around a circle in a certain unit such as centimeters. The formula to find the circumference, as stated, it 2πr, where r = radius.
» Application
In this case, we're asked to find the circumference of the circle using the formula 2πr. We're also given the radius as 10 cm.
» Solving
[tex]2(10)\pi[/tex] [tex]20\pi[/tex] 20π cmor
[tex]2(3.14)(10)[/tex] [tex](6.28)(10)[/tex] [tex]62.8[/tex] 62.8 cmAnswer:
c=2nr
but r=10 and n=3,14
c=2(3,14)(10)
c=62,8
four times the quotient of 3 divided by 4
Step-by-step explanation:
Step 1: Convert words into an expression
Four times the quotient of 3 divide by 4
We know that we are going to be multiplying 4 by something because in the statement we have four times. Reading further we also know that we are going to be dividing 4 from 3 which means that we will have 3/4. Finally, we see that we multiply our 3/4 by 4 which gives us our final solution.
[tex]4 * (3 / 4)[/tex]
If we want to solve it the 4's would just cancel and we would be left with 3.
3
Explanation:
You would start by dividing 3 by 4. Then multiply [tex]\frac{3}{4}[/tex] and 4. The 4s would cancel out leaving you with 3.
[tex]\frac{3}{4}[/tex] × [tex]4=3[/tex]
-3x° (2x7 - 4x + 1) multiply through polynomial
Answer:
-6x⁷ + 12x − 3
Step-by-step explanation:
Method 1 :
[tex]-3x^0\ (2x^7-4x+1)[/tex]
[tex]= (-3x^0)\times 2x^7-(-3x^0)\times4x+(-3x^0)\times1[/tex]
[tex]= (-3x^0)\times 2x^7+(3x^0)\times4x+(-3x^0)\times1[/tex]
[tex]=-6x^{0+7}+12x^{0+1}-3x^0[/tex]
[tex]=-6x^{7}+12x^{1}-3x^0[/tex]
[tex]=-6x^{7}+12x-3[/tex]
Method 2 :
Note : x⁰ = 1
[tex]-3x^0\ (2x^7-4x+1)[/tex]
[tex]=-3\ (2x^7-4x+1)[/tex]
[tex]=-3\times2x^7-(-3)\times4x+(-3)\times1[/tex]
[tex]=-6x^7+12x-3[/tex]
Supposea triangle has sides 3, 4, and5. Which of the following must be true? OA The triangle in question is not a right triangle. OB. The triangle in question is a right triangle. Oc.The triangle in question may or may not be a right triangle.
Answer: B. The triangle in question is a right triangle.
Reason:
The sides are
a = 3b = 4c = 5Plug them into the equation below and simplify both sides
[tex]a^2+b^2 = c^2\\\\3^2+4^2 = 5^2\\\\9+16 = 25\\\\25 = 25\\\\[/tex]
Therefore, we have a right triangle. For more information, check out the converse of the pythagorean theorem.
a) 3y = 43 + x
b) 8y + 5x = 61
Answer:
huh
Step-by-step explanation:
What is the probability of a customer buying a carrot at this store?
A 10%
B 19%
C 21%
D 27.5%
Answer: Its A
Step-by-step explanation:
You want to exchange £750 for euros. These are the currency exchange rates from 3 different sources. Company Exchange rate Travel Exchange 1.1065 Phoenix Financial 1.1050 Money Matters 1.1075 Which gives you the best value for money?
Money Matters is the best value for money for £750 they are giving 806.25 euros.
What is Money exchange?Customers can exchange one currency for another at a currency exchange, which is a licensed business.
The three agents are giving the money at different rates:-
Travel Exchange = 750 x 1.1065 = 798.75 Euros
Phoenix Financial = 1.1050 x 750 = 787.5 Euros
Money Matters = 1.1075 x 750 = 806.25 Euros
We can see that Money Matters is giving the best value for money.
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Can someone please help me with 6-10! I will give 100 points!!
Explanation:
6. A Linear function can be written in the form of f(x) = mx + b
7. In the form of f(x) = mx + b, the y intercept is b
8. The graph x = c is a vertical line with x intercept (c,0)
9. The graph y = c is a horizontal line with y intercept (0, c)
10. To find x intercept, let the y = 0, and solve for x
Answer:
See below ~
Step-by-step explanation:
Solutions :
===============================================================
6. A(n) linear function can be written in the form f(x) = mx + b.
===============================================================
7. In the form f(x) = mx + b, the y-intercept is b.
===============================================================
8. The graph of x = c is a vertical line with x-intercept (c, 0).
===============================================================
9. The graph of y = c is a horizontal line with y-intercept (0, c).
===============================================================
10. To find an x-intercept, let y = 0 and solve for x.
55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?
Answer:
r = 4/5
Step-by-step explanation:
Formula
Sum of an infinite geometric series = a / (1 - r)
Givens
Sum = 5*a
a = a
r = ?
Solution
5a = a/(1 - r) Divide both sides by a
5a/a = a / (a * (1 - r) The a's on the right cancel
5 = 1 / (1 - r) Multiply both sides by 1 - r
5*(1 - r) = 1*(1 - r)/(1 - r) The 1 - r s on the right cancel
5*(1 - r) = 1 Remove the brackets.
5 - 5r = 1 Subtract 5 from both sides
5-5 - 5r = 1 - 5 Combine
-5r = - 4 Divide by - 5
r = 4/5
Circle p has radius 8. Points Q and R lie on circle P, and the length of arc QR is 4pie. What is measure angle QPR in radians?
In the circle the measure of angle QPR in radians is π/4.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
The length of the arc QR is 4π, which is 1/2 of the circumference of the circle P.
Therefore, the circumference of the circle is -
2πr = 2π(8) = 16π
The angle subtended by the arc QR at the center of the circle is therefore -
θ = arc length / radius
θ = (4π) / 8
θ = π/2
Now, consider the triangle QPR.
The angle QPR at the center of the circle is equal to twice the angle subtended by the arc QR at any point on the circumference of the circle.
Therefore -
2∠QPR = θ = π/2
Solving for ∠QPR, we get -
∠QPR = (π/2) / 2
∠QPR = π/4
Therefore, the measure QPR is π/4.
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A coin is tossed three times. The probability of getting two heads and a tail is
_.
Give answer as a fraction in lowest terms.
The coin is an illustration of probability, and the probability of getting two heads and a tail is 3/8
How to determine the probability?The sample space of tossing a coin three times is:
S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
On the sample space, we have:
Two heads and a tail = 3
Sample size = 8
The required probability is then calculated using:
P = 3/8
Hence, the probability of getting two heads and a tail is 3/8
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I need help with question 10
Answer:
C
Step-by-step explanation:
pythagorean theorem: a²+b² = c²
area of square = length²
c = side opposite right angle = length of square Z
thus, area of square Z = c²
area of square X = a² (or b², it doesn't matter)
area of square Y = b² (or a²)
a² + b² = c²
region x + region y = region z
Hello
Please what’s the explanation to get the answer (2+2) ² (2+3)³
Answer:
141Step-by-step explanation:
Hello
Please what’s the explanation to get the answer (2+2) ² (2+3)³
we use PEMDAS
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
(2 + 2)² + (2 + 3)³ =
4² + 5³ =
16 + 125 =
141
PLEASE HELP ME ANSWER THIS FAST
Answer:
65 square yards
Step-by-step explanation:
5x5=25
5x4=20
5x4=20
20+20+25= 65
Donna borrowed $3000 from a bank for 2 years and was charged simple interest. The total interest that she paid on the loan was $120 . As a percentage, what was the annual interest rate of her loan?
Answer:
I = PRT / 100
P=3000R=?T = 2I = 120R = 100I/PT
R = 12000/6000
R = 2%
Which of the following represents the diameter of the circle below?
Answer:
xy represents the diameter
Concord Corporation sells its product for $7600 per unit. Unit variable cost are: manufacturing, $4400, and selling and administrative, $50. Fixed costs are: $14000 manufacturing overhead and $20000 selling and administrative. There was no beginning inventory at 1/1/21. Production was 20 units per year in 2021–2023. Sales were 20 units in 2021, 16 units in 2022, and 24 units in 2023. Net income under variable costing for 2023 is
The income under variable costing for 2023 for Concord Corporation is $73600.
How to calculate the net income?The formula to calculate the net income will be:
= Total sales - Total variable cost - Total fixed cost
= (7600 × 24) - (4400 + 50 × 24) - 2000
= 182400 - 106800 - 2000
= 73600
Therefore, the income under variable costing for 2023 for Concord Corporation is $73600.
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Seis menos el producto de cuatro y un numero x
La expresión matemática que representa la frase está dada por:
4x - 6.
¿Cuál es la expresión matemática que representa la frase?Vamos a resolverlo por partes:
El producto de cuatro y un numero x es dado por: 4x.Seis menos el producto es dado por: 4x - 6.Por lo tanto, la expresión es dada por:
4x - 6.
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What is the volume ?
Answer:
V≈523.6
Step-by-step explanation:
Volume is V=4/3*pi*r^3 and radius is half of diameter
Answer:
523.67km^3
Step-by-step explanation:
[tex]volume \: of \: a \: sphere = \frac{4}{3} \: \pi \: r {}^{3} \\ radiu \: r = \frac{10}{2} = 5km \\ volume = \frac{4}{3} \times 3.142 \times 5 {}^{3} \\ volume = \frac{1571}{3} = 523.67km {}^{3} [/tex]
If (x+3) is the factor of x3-6x2-11x+k then k is
[tex]f(x) = x^3 -6x^2 -11x +k \\\\\text{If (x +3) is a factor of f(x), then,}~ f(-3) = 0\\\\~~~~~~~f(-3) = 0\\\\\implies(-3)^3-6(-3)^2 -11(-3) +k = 0\\ \\\implies -27-54+33 +k=0\\\\\implies -48+k = 0\\\\\implies k = 48[/tex]
How much time will have elapsed from 2:37 to 3:19
Answer:
42min would have elapsed
Step-by-step explanation:
2:37-2:40 (3 min)
2:40-3:00 (20 min)
3:00-3:19 (19 min)
What is the surface area?
5 m
7 m
4 m
140 m squared
16 m squared
166 m squared
156 m squared
Answer:
c. 166
Step-by-step explanation:
area = l x w
surface area = area
A function is given. h(t) = −t + 6/5 ; t = −3, t = 1
Answer:
h(-3) = 4.2 or 21/5
h(1) = 0.2 or 1/5
Step-by-step explanation:
Plug in -3 for t.
-(-3) + 6/5 = 4.2 or 21/5
Plug in 1 for t.
-(1) + 6/5 = 0.2 or 1/5
Side AB is opposite which angle in triangle ABC?
Answer:
∠ACB
Step-by-step explanation:
we have three options for angles in triangle ABC:
- ∠CAB
- ∠ABC
- ∠ACB
∠ACB is the only angle out of the three given that doesn't directly touch side AB, so this must be our answer
if the ratio of nonfiction to fiction books on a bookshelf is 2 to 3. If the total number of books is 30, how many of them were nonfiction
Answer: 20
Step-by-step explanation: imagine the books in 10's cuz 30/3=10 and 2 of those tens out of the group of three are nonfiction, so that makes 20 out of 30
What is the value of 5x+3 when x=4?
A. 9
B. 12
C. 23
D. 60
Answer:
C. 23
Step-by-step explanation:
We substitue 4 for x then rewrite the expression as is
[tex]5(4)+3[/tex]
Then we solve [tex]5*4=20\\[/tex] [tex]20+3=23[/tex]
A cone has volume 3 pi, If the cone's radius in r, then what is the height?
Answer:
The formula for volume of a cone is area of a circle times height, divided by 3.
Therefore volume is pi times radius squared times height, divided by 3.
V = (3.14)(14)^2 (14)/3
V = (3.14) (196)(14)/3
V = (3.14) (2744)/3
V = 8616.16/3
V = 2872.05333
to the nearest hundredth is 2872.05 cubic yards.
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST 60 POINTS ∆PQR≅∆TUV. Find the missing measurements.
(PQ) = _______ (UV) = _______ m∠T= _______
m∠R= _______ (TV) = _______
m∠Q= _______ m∠U= _______
Answer:
(PQ) = (TU) (UV) = (QR) m∠T= m∠P
m∠R= m∠V (TV) = (PR)
m∠Q= m∠U m∠U= m∠Q
Step-by-step explanation:
Armando is a barber. He gets 40% of what each of his customers is charged. If the
customer leaves a tip, Armando gets 100% of the tip. How much does Armando earn on an
$8.50 haircut if the customer tips him $1.30?
Which points are on the graph of f(x)=2^x-3 Select each correct answer.(3, 1) (0, 1) (1, 3) (6, 8)
We can determine whether or not a point falls on the graph of a function by plugging its coordinates into the function equation.
If the right side is equal to the left side, the the equation is true, and the point does fall on the graph.
Solving the QuestionWe're given:
[tex]f(x)=2^x-3[/tex]Answer choices: (3, 1) (0, 1) (1, 3) (6, 8)(3, 1)[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]1=2^3-3\\1=8-3\\1\neq5[/tex]
(3,1) is not on the graph.
(0,1)[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]1=2^(0)-3\\1=1-3\\1\neq-2[/tex]
(0,1) is not on the graph.
(1,3)[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]3=2^(1)-3\\3=2-3\\3\neq-1[/tex]
(1,3) is not on the graph.
(6,8)[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]8=2^(6)-3\\8=64-3\\8\neq61[/tex]
(6,8) is not on the graph.
AnswerNone of the points are on the graph of the given function.
